"He's already indicated a degree of flexibility, and I think a sensible, balanced degree of flexibility," Commerce Secretary Wilbur Ross said on CNBC.

Despite fears from US allies and Washington Republicans that the measure could spark a trade war, Ross insisted the President's goal wasn't to drive the economy into chaos.

"I think you're going to see, as you understand the details of what actually is going to happen, that we're not trying to blow up the world. We're not trying to do that," Ross said.

He referred specifically to Trump's willingness to exclude Canada and Mexico from the tariffs as part of ongoing negotiations over the North American Free Trade Agreement. Trump spoke with Canada's Prime Minister Justin Trudeau on Monday, and the President's son-in-law Jared Kushner traveled to Mexico City for talks on Wednesday.

Trump hastily announced the steel tariffs last week during a meeting with industry executives, sending his aides into a scramble to fully vet the legality of the tariffs and finalize the language.

A bitter dispute ensued inside the West Wing, pitting advisers like Ross and trade adviser Peter Navarro against Gary Cohn, the director of the National Economic Council. Cohn had attempted to bring auto and beverage industry representatives -- end users of steel -- to the White House to lobby against the tariff. But his resistance angered Trump and Cohn announced his resignation on Tuesday.

Ross' comments make clear that the efforts to soften the tariffs may not be over, despite Cohn's departure.

Trump has heard from a slate of foreign leaders, including Canada's Trudeau, France's Emmanuel Macron, Germany's Angela Merkel and Britain's Theresa May, who have maintained the new tariffs would pose damaging effects for the economy.

In those conversations, Trump has indicated he hasn't made any final decision on the tariffs, according to people familiar with them. Publicly, however, he's taken a harder line.

"We're doing tariffs on steel. We cannot lose our steel industry. It's a fraction of what it once was. And we can't lose our aluminum industry; also a fraction of what it once was," he said during a news conference Tuesday with Sweden's Prime Minister, who also argued against new tariffs.